# [M1 Seminar II] Week 6 : Weighted a priori Estimates for Small Data

For the proof of the global existence theorem of nonlinear wave equations, this a priori estimates is essential as well as the high energy estimates. Also the high energy estimates play an important role in the proof of a priori … Continue reading

# [M1 Seminar II] Week 5 : High Energy Estimates

We prove the high energy estimates for the nonlinear wave equation on the nonlinearity $\alpha =1$. In fact, this problem is a special case of the quasi-linear symmetric hyperbolic system with some assumptions. By the help of the previous existence … Continue reading

# [M1 Seminar II] Week 1 : Local Existence for Quasi-linear Symmetric Hyperbolic Systems

This week, we prove the uniqueness and local existence for quasi-linear symmetric hyperbolic systems using general energy method. M1_Semi2_Week1

# [M1 Seminar] Week 6,7 : A Global Existence Theorem to the Linear Symmetric Hyperbolic Systems

This week, we prove the global existence theorem to the linear symmetric hyperbolic system by using the standard energy inequality. M1_Semi_Week6-7

# [M1 Seminar] Week 5 : Energy Estimates for the Linear Symmetric Hyperbolic System

We derive the corresponding estimates for higher derivatives from the basic energy estimates which was given in the last week. We also prove a simple corollary using this result. And we discuss about the finite propagation speed of the hyperbolic … Continue reading